This paper reports experimental results on the instability of thermocapillary convection in long half-zone liquid bridges of high Prandtl number fluids (Pr=67, 112 and 207 for 5, 10 and 20 cSt silicone oils, respectively). The experiments were carried out in microgravity on the International Space Station, which allowed sufficiently long waiting period for the development of instability. Critical temperature differences were measured for liquid bridges of 30 and 50 mm diameters and up to 62.5 mm length. The resultant critical Marangoni numbers (Mac) were obtained for a wide range of aspect ratio (=height/diameter), AR, up to AR=2.0. Linear stability analyses for Pr=67 were also carried out to obtain numerical data for comparison. The present experimental results for Pr=67 indicate 5.0×103<Mac<2.0×104 for large AR (AR>1.25) and they are in good agreement with the present linear stability analysis result. In contrast, the present results are considerably smaller than the previous data (Pr=74) taken in the Space Shuttle experiments. It is shown that this difference is due to the effect of heating rate of the liquid bridge. The data for oscillation frequency and azimuthal mode number are also presented. The non-dimensional oscillation frequencies as well as Mac for Pr=67 have shown a sudden decrease at around AR=1.25, suggesting the bifurcation of neutral stability curves.
Research Containing: Convection
Viscous fingering (VF) is an interfacial hydrodynamic instability phenomenon observed when a fluid of lower viscosity displaces a higher viscous one in a porous media. In miscible viscous fingering, the concentration gradient of the undergoing fluids is an important factor, as the viscosity of the fluids are driven by concentration. Diffusion takes place when two miscible fluids are brought in contact with each other. However, if the diffusion rate is slow enough, the concentration gradient of the two fluids remains very large during some time. Such steep concentration gradient, which mimics a surface tension type force, called the effective interfacial tension, appears in various cases such as aqua-organic, polymer-monomer miscible systems, etc. Such interfacial tension effects on miscible VF is modeled using a stress term called Korteweg stress in the Darcy's equation by coupling with the convection-diffusion equation of the concentration. The effect of the Korteweg stresses at the onset of the instability has been analyzed through a linear stability analysis using a self-similar Quasi-steady-state-approximation (SS-QSSA) in which a self-similar diffusive base state profile is considered. The quasi-steady-state analyses available in literature are compared with the present SS-QSSA method and found that the latter captures appropriately the unconditional stability criterion at an earlier diffusive time as well as in long wave approximation. The effects of various governing parameters such as log-mobility ratio, Korteweg parameters, disturbances' wave number, etc., on the onset of the instability are discussed for, (i) the two semi-infinite miscible fluid zones and (ii) VF of the miscible slice cases. The stabilizing property of the Korteweg stresses effect is observed for both of the above mentioned cases. Critical miscible slice lengths are computed to have the onset of the instability for different governing parameters with or without Korteweg stresses. These stabilizing properties of the Korteweg stresses captured in this present study are in agreement with the numerical simulations of fully nonlinear problem and the experimental observations reported in the literature.
Everybody is familiar with the action of gravity on a fluid where density gradients are present due to heating or compositional difference. Due to buoyancy, the denser portions sink to the bottom of the container, pushing away the lighter ones. As a result, convection sets in, transporting heat and mass. In weightlessness conditions, this driving force is absent but inertia exists as the tendency of a body to resist acceleration. When a container filled with liquid is subjected to high frequency vibrations, the fluid is not able to react due to inertia and this may create a flow. If the density is uniform, then the fluid moves as a solid body. However, when density gradient is present, also inertia will not be uniform, resulting in convective motion. Obviously, there is analogy between gravity-induced and inertia-driven convection, as a result of the Einstein equivalence principle, although the second one is almost unknown. What would be the impact of vibration on dispersion by molecular diffusion and heat transfer without buoyancy?
Geoflow: First Results from Geophysical Motivated Experiments inside the Fluid Science Laboratory of Columbus
Objective of GeoFlow experiment is to study thermally-driven rotating fluids, in order to investigate the stability, pattern formation, and transition to turbulence of viscous incom-pressible fluids contained between concentric, co-axially rotating spheres. These physical mechanisms are important for a large number of astrophysical and geophysical problems showing flows in spherical geometry driven by rotation and convection: for example, to explain the mantle convection of the Earth, or the flow in a planet's interior. The European microgravity experiment GeoFlow, which is executed in the Fluid Science Laboratory (FSL) of Columbus module on the International Space Station (ISS), is an experiment investigating pattern formation and stability of thermal convection in rotating spherical shells under the influence of an artificial central symmetric buoyancy field and eliminated gravity. In this paper we present numerical preliminary studies of this spherical Rayleigh-Bnard problem under a central dielectrophoretic force in microgravity environment and first experimental results from ISS. Numerical simulations are done for a range of parameter values for Rayleigh and Taylor number. For the experiment flow visualization is realized using the Wollaston-shearing method.
This paper reports some important results obtained from a series of microgravity experiments on the Marangoni convection that takes place in liquid bridges. This project, called Marangoni Experiment in Space (MEIS), started from August 22, 2008 as the first science experiment on the Japanese Experimental Module “KIBO” at the ISS. Two series of experiments, MEIS-1 and 2, were conducted in 2008 and 2009, respectively. The experimental methods used are explained in some detail. The maximum size of the liquid bridge that could be realized during these experiments was 30 mm in diameter and 60 mm in length, giving an aspect ratio of 2.0. The results are obtained for a wide range of aspect ratios of the liquid bridges, including the values that cannot be reached in 1 g experiments, and therefore, they provide indispensable amount of data for the study of instability mechanisms of the Marangoni convection.
An alloy semiconductor Si1−xGex (x~0.5) crystal was grown by the TLZ method in microgravity. Ge concentration was 48.5±1.5 at% for the whole region of 10 mm diameter and 17.2 mm long crystal. Compositional uniformity was established but the average concentration was a little deviated from the expected 50 at%. For further improving compositional uniformity and for obtaining Si0.5Ge0.5 crystals in microgravity, growth conditions were refined based on the measured axial compositional profile. In determining new growth conditions, difference in temperature gradient in a melt, difference in freezing interface curvature, and difference in melt back length of a seed between microgravity and terrestrial growth were taken into consideration.
A Si0.5Ge0.5 crystal was grown on board the International Space Station (ISS) using the traveling liquidus-zone method. Average Ge concentration was 49±2 at% for the growth length of 14.5 mm. Radial compositional uniformity was excellent especially between the growth length of 3 and 9 mm; concentration fluctuation was less than 1 at%. In this experiment, cartridge surface temperatures were monitored and heater temperatures were adjusted based on the monitored temperatures for improving compositional uniformity of a grown crystal. A step temperature change by 1 °C was imposed for adjusting heater temperatures. This procedure made it possible to observe growth interface shape; striations due to heater temperature change were observed by a backscattered electron image. Growth rates were precisely determined by the relation between interval of heater temperature change and the distance between striations. Based on the measured growth rates, two-dimensional growth model for the traveling liquidus-zone method was discussed.
A silicon germanium mixed crystal Si1−xGex (x~0.5) 10 mm in diameter and 9.2 mm in length was grown by the traveling liquidus-zone (TLZ) method in microgravity by suppressing convection in a melt. Ge concentration of 49.8±2.5 at% has been established for the whole of the grown crystal. Compared with the former space experiment, concentration variation in the axial direction increased from ±1.5 at% to ±2.5 at% although average Ge concentration reached to nearly 50 at%. Excellent radial Ge compositional uniformity 52±0.5 at% was established in the region of 7–9 mm growth length, where axial compositional uniformity was also excellent. The single crystalline region is about 5 mm in length. The interface shape change from convex to concave is implied from both experimental results and numerical analysis. The possible cause of increase in concentration variation and interface shape change and its relation to the two-dimensional growth model are discussed.
First identification of sub- and supercritical convection patterns from ‘GeoFlow’, the geophysical flow simulation experiment integrated in Fluid Science Laboratory
Physical mechanisms of thermally driven rotating fluids are important for a large number of geophysical problems, e.g. to explain the convection of the Earth's liquid outer core. Objective of the ‘GeoFlow’ experiment is to study stability, pattern formation, and transition to chaos of thermal convection in fluid-filled concentric, co-axially rotating spheres. This experiment is integrated in the Fluid Science Laboratory of the European COLUMBUS module on International Space Station. Fluid dynamics of the experiment was predicted with numerical simulations by means of a spectral code. In the non-rotating case the onset of convection bifurcated into steady fluid flow. Here patterns of convection showed co-existing states with axisymmetric, cubic and pentagonal modes. Transition to chaos was in the form of sudden onset. For the thermal convection in rotating spheres the onset of first instability showed an increase of modes for higher parameter regime. Transition was from steady via periodic to chaotic behaviour. Convection patterns of the experiment are observed with the Wollaston shearing interferometry. Images are in terms of interferograms with fringe patterns corresponding to special convective flows. A first glance at the images showed the classification of sub- and supercritical flow regimes. Aligned with numerical data a shift between experiment and numerical simulation was identified. Identification of convection patterns in interferograms was demonstrated for the example of a supercritical flow.
Experimental and numerical analysis of mass transfer in a binary mixture with Soret effect in the presence of weak convection
One of the targets of the experiment IVIDIL (Influence Vibrations on Diffusion in Liquids) conducted on-board ISS was to study the response of binary mixtures to vibrational forcing when the density gradient results from thermal and compositional variations. Compositional variations were created by the Soret effect and can strengthen or weaken the overall density gradient and, consequently, the response to vibrational forcing. We present the results of two experimental runs conducted on-board ISS in the frame of the experiment IVIDIL for low and strong vibrational forcing. The experimental observations revealed that a significant mean flow is set within 2 minutes after imposing vibrations and later in time it varies weakly and slowly due to the Soret effect. A mathematical model has been developed to compute the thermal and concentration fields in the experiment IVIDIL and verify the accuracy of picture processing based on the classical approach used in non-convective systems with the Soret effect. The effect of temperature and concentrations perturbations by joint action of vibrational convection and Soret effect on long time scale are carefully examined. The model demonstrates that image processing used for non-convective systems is suitable for the systems with vibration-affected thermodiffusion experiment.